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Grade 12 math help please!! For what value of b will the polynomial p(x) = 2x^3 + bx^2  5x +2 have the same remainder when it is divided by x  2 and x+1?
 one year ago
 one year ago
Grade 12 math help please!! For what value of b will the polynomial p(x) = 2x^3 + bx^2  5x +2 have the same remainder when it is divided by x  2 and x+1?
 one year ago
 one year ago

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TAKEBACKMATHBest ResponseYou've already chosen the best response.0
okay I will show you:
 one year ago

pottersheepBest ResponseYou've already chosen the best response.1
thank you so much!
 one year ago

TAKEBACKMATHBest ResponseYou've already chosen the best response.0
sorry, it too late for me I will hand this over to lonesome else?
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
Here it goes~ Have you learnt remainder theorem yet?
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
@pottersheep Are you there??
 one year ago

pottersheepBest ResponseYou've already chosen the best response.1
Yes sorry, we have!
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
So, let R be the remainder when p(x) is divided by x2. By remainder theorem, what would you get? I mean p(_) = ...?
 one year ago

pottersheepBest ResponseYou've already chosen the best response.1
So i'd sub in 2 for x
 one year ago

pottersheepBest ResponseYou've already chosen the best response.1
Sorry what do I do with the b though?
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
Right, so for p(2), you get p(2) = 4b  24 = R, agree? (By remainder theorem, p(a) = R , when p(x) is divided by xa)
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
And what is the remainder when p(x) is divided by x+1 ?
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
Not really.. Remainder = p(1) = 2(1)^3 + b(1)^2  5(1) +2 = ...?
 one year ago

pottersheepBest ResponseYou've already chosen the best response.1
Opps, sorry! I subbed in 1!
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
Yes. Note that the remainder is p(x) = R when p(x) is divided by xa. Now, p(x) is divided by x+1, so a = 1 in the case. [ x(1) = x+1]
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
From the question, the polynomial p(x) = 2x^3 + bx^2  5x +2 have the same remainder when it is divided by x  2 and x+1. So, equate the two remainder you got and solve b. Got it?
 one year ago

pottersheepBest ResponseYou've already chosen the best response.1
Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!
 one year ago

CallistoBest ResponseYou've already chosen the best response.1
Yes. Since they have the SAME remainder! You're welcome :)
 one year ago
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